What is the derivative of (5x-3^4(2x-7)^{-3}) ?

The derivative of (5x-3^4(2x-7)^{-3}) is (20(5x-3)^3)/((2x-7)^3)-(6(5x-3)^4)/((2x-7)^4)

What is the first derivative of (5x-3^4(2x-7)^{-3}) ?

The first derivative of (5x-3^4(2x-7)^{-3}) is (20(5x-3)^3)/((2x-7)^3)-(6(5x-3)^4)/((2x-7)^4)

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\frac{d}{d x} ((5 x - 3)^{4} (2 x - 7)^{- 3})

\frac{20 ( 5 x - 3 ) ^{3}}{( 2 x - 7 ) ^{3}} - \frac{6 ( 5 x - 3 ) ^{4}}{( 2 x - 7 ) ^{4}}

Solution steps

\frac{d}{d x} ((5 x - 3)^{4} (2 x - 7)^{- 3})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (5 x - 3)^{4}, g = (2 x - 7)^{- 3}

= \frac{d}{d x} ((5 x - 3)^{4}) (2 x - 7)^{- 3} + \frac{d}{d x} ((2 x - 7)^{- 3}) (5 x - 3)^{4}

\frac{d}{d x} ((5 x - 3)^{4}) = 20 (5 x - 3)^{3}

\frac{d}{d x} ((2 x - 7)^{- 3}) = - \frac{6}{( 2 x - 7 ) ^{4}}

= 20 (5 x - 3)^{3} (2 x - 7)^{- 3} + (- \frac{6}{( 2 x - 7 ) ^{4}}) (5 x - 3)^{4}

Simplify

20 (5 x - 3)^{3} (2 x - 7)^{- 3} + (- \frac{6}{( 2 x - 7 ) ^{4}}) (5 x - 3)^{4} : \frac{20 ( 5 x - 3 ) ^{3}}{( 2 x - 7 ) ^{3}} - \frac{6 ( 5 x - 3 ) ^{4}}{( 2 x - 7 ) ^{4}}

= \frac{20 ( 5 x - 3 ) ^{3}}{( 2 x - 7 ) ^{3}} - \frac{6 ( 5 x - 3 ) ^{4}}{( 2 x - 7 ) ^{4}}

(\frac{1}{2 x})^{^{'}}

d er i v a t i v e θ cos (θ)

\int (2 x - 4^{x}) d x

a re a y = x^{2} - 4, y = 5

\frac{d}{d x} (8^{s i n (π x)})

What is the derivative of (5x-3^4(2x-7)^{-3}) ?
The derivative of (5x-3^4(2x-7)^{-3}) is (20(5x-3)^3)/((2x-7)^3)-(6(5x-3)^4)/((2x-7)^4)
What is the first derivative of (5x-3^4(2x-7)^{-3}) ?
The first derivative of (5x-3^4(2x-7)^{-3}) is (20(5x-3)^3)/((2x-7)^3)-(6(5x-3)^4)/((2x-7)^4)